Fuzzy Controler MAP

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1060 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39. NO . IO. OCTOBER 1992

Fuzzy Control of Mean Arterial Pressure inPostsurgical Patients with SodiumNitroprusside InfusionH a o Y i n g , Member , IEEE, Michae l McE ache rn , Dona ld W . E ddleman , Member, IEEE,

L ouis C . Sheppa rd , Fellow, IEEEAbstract-We developed a fuzzy control system to provideclosed-loop control of mean arterial pressure (MAP) in post-surgical patients in a cardiac surgical intensive care unit settingby regulating sodium nitroprusside (SNP) infusion. The fuzzycontroller, originally expert-system-based, was analyticallyconverted to ten nonfuzzy control algorithms, which reducedexecution time dramatically. The core of the control algorithmswas a nonlinear proportional-integral (PI) controller whoseproportional gain and integral gain adjusted continuously ac-cording to error and rate change of error of the process output.The gains became larger when process output was far from de-sired setpoint and smaller when process output was close to de-sired setpoint, resulting in more dynamic and stable controlperformance than the regular PI controller, especially when a

linear process with time-delay or a nonlinear process was in-volved. The control algorithms, encoded in C programminglanguage, were implemented to control MAP in patients. Pre-liminary clinical results showed that the average percentage oftime in which MAP stayed between 90%and 110%of the MAPsetpoint was 89.31%, with a standard deviation of4.96%.Thesewere calculated based on 12patient trials, with total trial timeof 95 and 13 min.I . INT RODUCT ION

HE fast-acting vasodilator drug sodium nitroprussideT ( s N P ) is used to trea t patients who demonstra te e le-vated systematic arterial blood pressure after open-heartsurgery. The rapid and powerful action of SNP imposesupon nursing personnel the task of frequent monitoring ofmean arterial pressure (MA P) followed by adjustment ofSN P infusion rate. Because nurses have many other du-ties, inappropriate or infrequent control actions on SNPadjustment may occur, which may lead to poor systemperformance.To improve the quality of patient care, automaticclosed-loop control SN P delivery systems have been de-veloped. A nonlinear proportional-integral-derivativeManuscript received February 13, 1991; revised November 1 8 , 1991.H. Ying was with the Department of Biomedical Engineering, Univer-sity of Alabama at Birmingham, Birmingham, A L 35294. He is now withthe Department of Physiology and Biophysics, Biomedical EngineeringCenter, and Office of Academic Computing, University of Texas MedicalBranch, Galveston, TX 77555.M. McEache m and D. W . Eddleman are with Kemp-Carraway HeartInstitute, Carraway Methodist Medical Center, Birmingham, AL 35234.L. C. Sheppard was with the Department of Biomedical Engineering,University of Alabama at Birmingham, Birmingham, AL 35294. He is nowwith the University of Texas Medical Branch, Galveston, TX 77555.

(PID ) control system was first built and used clinically inthe mid- 1970s [9]. A similar control system w as also im-plemented clinically later [2]. Various control algorithmsincluding nonlinear adaptive control, multiple-modeladaptive control and adaptive multivariable control weredeveloped and tested [3], [ 5 ] - [ 8 ] , [12], [13]. Clinicalstudy indicated that automatic control was effective andsuperior to manual control [l], [2]. Furthermore , as theresult of over six years of intensive collaborative effortbetween IVACTMCorporation and The Cleveland Clinic,IVAC Corporation began marketing its TITRATORTMSNP Closed Loop Module Model 10K n recent years.The success of developing the above-mentioned drugdelivery control sy stems, especially the adaptive controlsystems, heavily depended on mathematical models of pa-tients. However, accurately identifying a mathematicalmodel of patients is a very difficult task, due to the com-plexity of the human body. Modelling a process is noteasy. Even if a process model is available, it may still bechallenging to design an appropriate controller to achievedesired system performance. Fo r a simple linear processwithout time-delay , designing a suitable linear controlleris relatively easy. However, if a process involves time-delay, nonlinearity, or time-variance, a suitable controllermay b e difficult to design. For these kinds of processes,nonlinear controllers normally perform b etter than linearcontrollers do. But, designing nonlinear controllers ismuch m ore difficult because of the lack of general nonlin-ear control theory. To control complex systems involvingtime-d elay, nonlinearity or time-va riance, fuzzy control-lers may be needed, because they can be constructed em-pirically without explicit mathematical models of the pro-cesses involved.Following the invention of fuzzy set theory in 1965[191, the first fuzzy controller was developed in 1974 [4] .Fuzzy contro llers are linguistic if-then rule-based and canbe designed using control operators knowledge and ex-perience about processes. A fuzzy controller can thus beregarded as an expert system employing fuzzy logic forits reasoning. Fuzzy controllers, being generally nonlin-ear, provide an alternative means to solve time-delay,nonlinear and time-variant control problems whethermathematical models of processes involved are available

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YING et al . : FUZZY CONTROL OF MEAN ARTERIAL PRESSURE 1061

Biological systems such as the human body involvetime-delay , nonlinearity and time-variance. Designingappropriate controllers for such systems based on existingnonfuzzy control theories is very challenging and time-consuming. The fact that human operators like medicaldoctors and other clinical personnel can control variousphysiological parameters of the human body successfullyby using their knowledge and experience suggests thepossibility of using fuzzy controllers in these situations.Because fuzzy controllers are linguistic rule-based andhave much in common with expert systems, expertsknowledge and experience can be incorporated into thefuzzy controllers. Merg er of fuzzy controllers and expertsystems will prov ide potent controllers that are capable oflearning, adapting, and self-organizing. These types ofcontrollers may be useable for complicated biologicalcontrol problems that are solvable by human operators butunsolvable by existing nonfuzzy controllers.We had previously developed a generalized expert-sys-tem-shell-based fuzzy controller [151, which we then uti-lized to control M A P by regulating S N P infusion, in bothdigital computer simulation and real-time in pigs [161,[171. The encouraging results of this previous research offuzzy control of M A P clearly indicated that success offuzzy control M A P in patients was achievable. The re-sults of fuzzy control of M A P in postsurgical patientsclinically, which is the first use of a fuzzy controller in aclinical setting, is reported in this paper.

11. ME T H O D S N D M A T E R I A L SA. Reduction of Execution Time of the Expert-System-Shell-Based Fuzzy Controller by Analytically ConvertingIt to a Group of Nonfizzy Control Algorithms

The fuzzy controller that we used in compu ter simula-tion and real-time animal experiments was based on ageneral-purpose fuzzy logic production system shell(FLOPS) [15]. Although the fuzzy controller could takethe advantage of the capabilities of the expert system shelland could change its structure flexibly by utilizing differ-ent rules and com mands of the expert system shell, i t wasslow in execution time. To m ake real-time fuzzy controlof MAP in patients possible, we analytically convertedthe expert-system-shell-based fuzzy controlle r into non-fuzzy control algorithms. The conversion was to reduceexecution time considerably and reveal the structure ofthe fuzzy controller. The method of the conversion isbriefly described and the result of the conversion is givenin this section. Detailed information is available in a pre-vious paper [181.Designating M A P ( n T ) an d M A P(nT - T ) as M AP atsampling time nT an d nT - T respectively ( T s samplingperiod), the inputs of the fuzzy controller could be rep-resented as

e (nT) = M A P(nT) - setpoint ( 1 )r ( n T ) = [M A P(nT) - MAP(nT - T ) ] / T (2 )

where the setpoint was the desired M A P level. Theexpert-system-shell-based fuzzy controller was mad e upof following six components.The first compo nent scaled the inpu ts, e ( n T ) an d r ( n T ) ,respectively by multiplying G E , the scalar for error ofM A P , an d G R , the scalar for rate change of error of M A P ,to obtain scaled inputs, G E . e ( n T ) an d G R * r ( n T ) .The second com ponent comp rised the fuzzification al-gorithms illustrated in Fig. l that fuzzified G E * e ( n T ) ndG R * r ( n T )o obtain fuzzy sets for the inputs. In our study,the same fuzzification algorithm was used to fuzzifyboth scaled inputs. This yielded a fuzzy set forG E . e ( n T ) ( G R . r ( n T ) ) , - ( n T ) r - ( n T ) ) ,which was as-sociated with two memberships for two members of thefuzzy set respectively, p e + (F ~ + for positive andp , - ( p , - ) for negative.The third component contained the four fuzzy controlrules listed below that linguistically related the fuzzy setsfor inputs to the fuzzy set for incremental S N P infusionrate, GSNP-(nT).

If e - ( n T ) is positive and r ( n T ) s positiveif e - ( n T ) is positive and r ( n T ) is negativeif e ( n T ) is negative and r ( n T ) is positiveif e - ( n T ) is negative and r - ( n T ) is negative

then GSNP-(nT) is negative; orthen GSNP-(nT) is zero; orthen GSNP-(nT) is zero; orthen GSNP-(nT) is positive . 0.4)

( r l )( r2 )(r 31

The fuzzy set GSNP(nT), shown in Fig. 2 , had threememb ers, namely positive, ze ro, and negative. The fourth component was Zadeh A N D an d OR fuzzylogic [19]A N D ( C L I , 2 ) = m i n ( p l , 112)

OR(111, 112) = max(CLI9 112)(3)(4)that defined the relation of the if-part with the then-partin the fuzzy control rules, r l to r4. H ere pl and p 2 are twomemberships of fuzzy sets while min (max) is a fuzzylogic op erator which yielded smaller (larger) membershipbetween p, an d p 2 . Zadeh A N D was used to evaluate theindividual fuzzy control rules, and Zadeh OR was used toevaluate the implied OR between fuzzy control rules 1-2and 1-3.The fifth component defuzzified the fuzzy setGSNP-(nT) into a crisp incremental S N P infusion rate,GSNP(nT),using the following defuzzification algorithm:(5)/%SNP+ -k PCBSNP- l L

P6SNP-t + hSNPO+ PCBSNP-GSNP(nT) =

where pgsNp+,GSNP0 nd pBSNP-were the membershipscorresponding to the respective members of positive,zero, and negative of the fuzzy set G SN P ( n T ) .These memberships were generated by th e four fuzzy con-


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1062 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 39, NO . 10, OCTOBER 1992

membershipnegative positivel o 0 T72o o / -~ ~ ~ ~ _ _caled inputs

- 3 , -2 4 -; E -s 8 24 32 GE*e(nT) . GR*r(nT)(-L) (L )

Fig. 1 . Fuzzification algorithm for the inputs of the fuzzy controller, scalederror, GE e ( n T ) , and scaled rate change of error, GR . r ( n T ) ,of MAP.The fuzzy sets have two members, posit ive and negative .

membership negative positive

0 7 5

- __ - - - -. - incremental SNP-j, -i 4 -i 6 -8+ 8 i4 infusion ra te , 6SNP(nT)(-U (L)

Fig. 2 . Fuzzy set for the incremental SN P infusion rate, GSNP-(nT). Thefuzzy set has three members, pos itive, ze ro, and nega tive.

trol rules. L, defined both in Figs. 1 an d 2 , was a turningThe last component scaled GSNP(nT) by GI, th escalar for incremental SNP infusion rate, to obtain a scaledincremental SNP infusion rate, GI GSNP(nT).GI*GSNP(nT)was then multiplied by sampling time T an dwas then added to SNP(nT - T), th e SNP infusion rateat sampling time nT - T , to get a new SNP infusion rate,SNP(nT). That is

point of the fuzzy sets. I C 1 8

IC13

I IC12

-LSNP(nT) = SNP(nT - T ) + GI * GSNP(nT) T. (6)To analytically convert the above-described expert-sys- IC14tem-shell-based fuzzy controller to a group of nonfuzzycontrol algorithms, the phase plane of the scaled inputs,GE.e(nT) an d G R . r ( n T ) , were divided into 2 0 differentregions, shown in Fig. 3. In the figure, IC stands for inputcombination and IC x means input combination N o. x . T o IC15c 19

GRr(nT)IC11/\

LIC16

I C 1 7

IC10

GEe(nT)LIC 9

IC20show how the conversion worked, lets take IC 2 as anexample. Suppose that the memberships obtained by usingthe fuzzification algorithm shown in Fig . 1are pe+ an dpew for the scaled error G E * e ( n T ) , nd p,+ an d p r - fo rthe scaled rate change of error GR r ( n T ) Here pe+ an dpep are the respective memberships for th_e memberspositive and negative of the fuzzy set e ( n T ) whilep r + an d p r - are the respective m emberships for the mem-bers positive and negative for the fuzzy set r - ( n T ) .Note that for scaled inputs in the IC 2 region,

0 I R - r ( n T )5 GE.e(nT) 5 L. (7)

Fig. 3. Input combination (IC) of scaled error, G E . e ( n T ) ,and rate changeof error, G R . r ( n T ) ,of MAP. L = 16, as shown in Fig. 1 .

Therefore according to Fig. 1, pe+ 2 p,+ ay d pe - I , - .The memberships for the fuzzy set GSNP ( n T ) can beobtained by using Zadeh A N D an d OR fuzzy logic.positive or GSNP-(nT) with membership pe- , (8)

(9)(10)

zero of GSNP-(nT) with membership p r - ,negative of GSNP-(nT) with membership p r + .


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Be aware that Figs. 1 an d 2 can be expressed as TABLE IT H E C A L E DNCREMENTALN P INFUS IONRAT E F TH E FUZZYCONTROLLER, GI .GSNP(nT), FO R TH E DIFFERENTCALED INPUT( 1 1 )( 1 2 )

CoMBiNATioNs (IC) ILLUSTRATED I N FIG. 3 . GI is TH E SCALAR FORGSNP(nT). GE AN D GR A R E TH E S C A L A R SO R TH E INPUTS , e ( n T ) AN DrcnT), RESPECTIVELY., ILLUSTRATEDN FIGS.AND?, IS TH E T U R N I N GPOINT F TH E F U Z Z Y E T S , ( n T ) AN D r ( n T )

p e + = [GE*e(nT)+ L] /2Lp e - = 1 - pe+

Scaled Incremental SNPp,+ = [GR-r(nT)+ L] /2L (13)

Input Combinations (IC)p r - = 1 - p r + . (14) of the Scaled Inputs Infusion Rate, GI.GSNP (nT)Substitute thethrough (10) intocan then simplify

net

see equation (16)see equation (17)- [ G R . r ( n T ) + L ] . G I / 2- [ G E . e ( n T ) + L ] . G I / 2- [ G R . r ( n T ) - L ] . G I / 2- [ G E . e ( n T ) - L ] . G I / 2memberships in the expressions (8 )the defuzzification algorithm (5). W ethe algorithm by utilizing ( 1 1)- ( 14) to

IC13C3, IC29C4 , IC7, andnd IC6C8Ic9 and IcloI C I 1 and 1c1 2IC 13 and IC 14IC15 and IC16IC17 - L .G IIC18 0

5 - c

L-GIGSNP(nT) = - 3L - GE-e(nT) IC19 L.GIIC20 0

* [GE.e(nT) + GR.r(nT)]. (15)Similarly, we can convert the expert-system-shell-basedfuzzy controller to nonfuzzy control algorithms for otherinput combinations. A tota l of ten different nonfuzzy con -trol algorithms for 20 different input combinations can beobtained; these are listed in Table I.It should be noted that these nonfuzzy control algo-rithms are the analytical description of the expert-system-shell-based fuzzy controller. Therefore, they precisely

If the fuzzy controller is appropriately designed, MAPshould stay in these input combin ation regions most of thetime and gradually approa ch the origin of the phase planeof GE.e(nT)an d GR.r(nT)(e(nT)= 0 an d r ( n T ) = 0).Comparing (16) an d (17) to the proportional-integra1(PI) control algorithm in the discrete-time formGSNP(nT) = - [ K j - e(n T ) + K, r(nT)] ( 1 8 )- -represent the fuzzy controller. Usually, such precise rep-resentation is not .possible because the structures of fuzzy

tha t they can not be de-scribed analytically.The resultant ten control algorithms discussed abovewere employed in the patient trials. The control algo-

where K p an d Ki re the proportional gain and integralgain, the fuzzy controller can clearly be regarded as anonfuzzy nonlinear PI controller, with a proportional gainreL-GIsGR or L-GIaGRKpd = 3L - GE.le(nT)I 3L - GR. r ( n T ) )rithms were encoded in C programming language and theexecution time for each input was only a fraction of asecond. Not only was the execution time reduced dra-matically but the time used to design the control systemwas also reduced. The analytical expressions shown inTable I enabled us to analyze the structure of the fuzzycontroller as well as the role of the different components

and parameters of the fuzzy controller.B. Nonlinear Characteristic of the Fuzzy Controller

Among the ten control algorithms discussed above, themost important in affecting performanc e are two nonlinearcontrol algorithms corresponding to the input combina-tions of scaled inputs ICl , IC2, IC5, an d IC6 an d IC3,IC4, IC7 and IC8 shown in Fig. 3.If GR. r ( n T ) J5 GE. Je (nT)JI ,L*GI

3L - GE.(e(nT)ISNP(nT) = -[GE-e(nT)+ GR.r(nT)] (16)

if GE . (e(nT)II R. r ( n T ) (I ,L-GI

3L - GR. r ( n T ) JSNP(nT) = -* [GE*e(nT)+ GR.r(nT)]. (17)

(19)and an integral gain

L.GI * GE3L - GE*(e(nT)I

L*GI* E3L - GR. r (nT)lK. = orid

(20)continuously changing with error, e(nT),and rate changeof error, r ( n T ) , of the system output. When M AP is in asteady state, that is, when e ( n T ) = 0 an d r ( n T ) = 0, (16)and (17)become

GI3SNP(nT) = -- [GE e ( n T ) + GR * r(nT)] (21)

which is a PI controller with K p = GI - G R /3 an d K j =GI GE/3. If MAP is not in a steady state, K pdan d Kidin (19)and (20)are always greater than the respective Kpand Ki of the corresponding PI controller. That isKpd Kid - 3L- = - -Kp Ki 3L - GE.(e(nT)( ' '

if GR.Ir(nT)(I E.le(nT)(I (22)3LKpd - Kid -Kp Kj 3L - G R * ( r ( n T ) J ''

if GE. e(nT)I I R. r(nT)I I . (23)


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The larger e(nT) and r( nT ) are, the greater the differencebetween Kpdan d K,(K,, an d K , ) . Nevertheless, the maxi-mum difference is reached when GE . (e(nT )( = L and/orG R . 1 r(nT)1 = L . At these points, Kpd an d K,d are GI *GR /2 and GI GE /2 , respect ively, which are 50% argerthan the integral gain and the proportional gain, namelyK p = GI * G R / 3 a nd K , = GI * GE /3 , associated witha corresponding PI controller.The nonlinearity of the fuzzy controller expressed in(1 6) and (17) can be also changed by using different val-ues of GE, GR, and L. As one extrem e, if the value of L+ 03, then Kpd -+ K p an d Kld + K , , which means thefuzzy controller becomes the PI controller. On the otherhand, the smaller the value of L , the more nonlinear thefuzzy controller is.The controller may switch from on e control algorithmto another in Table I, depending on the change of inputcombination from time to time. Howev er, the switchingis always continuous and sm ooth on the boundaries of twoor more adjacent input combinations involved. For ex-ample, on the boundary between IC6, IC7, IC14, IC15,and IC19 on which GE*e(nT) = - L a nd G R . r ( n T ) =- L , any control algorithm for the input combinations in-volved produces the same GSNP(nT) as others do.Two of the control algorithms shown in Table I imposerestraints on maximu m increment and decrement of S NPinfusion rate for any sampling period. T he maximum dec-rement, L GI T , is reached when the scaled inputs arein the IC19 region. The maximum increment, - L * GIT, is earned when the scaled inputs are in region IC17.For the values of the parameters we c hose, L = 16, GI =-0.06, and T = 10 s (the choice of these values will bediscussed in the next section), the maximum incrementwas 9.6 mL/h and the maximum decrement was 9.6m L / h . It should be noted that the restraints are charac-teristics of the fuzzy controller itself rather than safetymechanisms built in by the authors.The understanding of the structure and the role of theparameters of the fuzzy controller made it more effectiveto design the fuzzy control SNP delivery system for pa-tients by utilizing approp riate nonlinearity and the valuesof the adjustable parameters of the fuzzy controller.

C. Design of Fuzzy Control SNP Delivery System Basedon Computer SimulationThe nonlinearity of the fuzzy contr oller discussed abovewas desirable because the controller was to deal withMAP, which was an unknown function involving time-delay , nonlinearity and time-varian ce of many physiolog-ical variables of the human body. However, the nonlin-earity of the fuzzy controller had to be confined within anadequate range. This confinement was important in order

to adapt to a wider range of the patients dynamic param-eters, and to restrict adverse effects possibly associatedwith the nonlinear fuzzy controller. Most importantly,properly limiting the range of the nonlinearity and thusavoiding some possible unstable states of the fuzzy con-

trol system improved safety of the patients who were ex-tremely sensitive to SNP .There are five adjustable parameters of the fuzzy con-troller, namely G E, GR , GI, L and T, which significantlyaffect the performance of the fuzzy controller. Based onour previous ex perience, a sam pling period of ten secondswas used fo r the patient trials. To deter mine the effect ofadjusting the other parameters, the mathematical modelin Laplace transfer function describing the relationshipbetween SN P infusion rate, SNP(s), and change in MA Pin pat ients , GMAP(s) [ lo ] , [ I l lGMAP(s) - Ke-30s(l + 0.4eC5OS)

was used in computer simulation. K represented the sen-sitivity of patients to SNP. K is -0.72 for the normalpatients, -0.18 for the insensitive patients and -2.88 forthe sensitive patients [101.As stated in the last section, the nonlinearity of thefuzzy controller can be adjusted by changing the param-eters of the controller, GE , GR , and L (GI doe s not affectnonlinearity). The equations (16 ) and (17) were utilizedto guide tuning of the parameters. The larger GE an d/orGR values are, the more nonlinear the fuzzy controller iswhen L is fixed. We chose the same GE and GR valuesas those used in the pig experimen ts [171 for initia l patienttrials, that is, GE = 0.25 and GR = 8.0. W e increased Lfrom 1 0, used in the previous study, to 16 to avoid pos-sibly excessive overshoot of MAP for the sensitive pa-tients. Fig. 4 illustrates the effect of the incre ase in L valueon the performance of M AP when the sensitive patients( K = -2.88) were tested. The overshoot of MAP waslowered from 1 6.4 % for L = 10 to 13.2% for L = 16 .After the determination of T, GE , GR, and L values,the value of the scalar for incremental S NP infusion rate,GI, was to be set. GI should be a negative number sincethe patient sensitivity, K , is negative. According to (16)and (17), GI changes the overall gain of the fuzzy con-troller. As indicated by (19) and (20), the larger the ab-solute value of G I, the greater the nonlinear proportionalgain Kpdand integral gain K,d of the fuzzy controller. To olarge an absolute value of GI may cause the SN P controlsystem to become unstable. This is especially true whenpatients ar e extremely sensitiv e to SN P. Th e GI value usedin the computer simulation and the pig experiments was-0.08. To attenuate possible large overshoot of MAP andimprov e the patients safety , the GI value used in the pa-tient trials was -0.06. The effect of GI = -0 .08 and GI= -0 .06 on the performance of MA P for both the sen-sitive patients ( K = -2.88) and the normal patients ( K= -0.72) is shown in Figs. 5 and 6, respectively. Ac-cording to Figs. 5 and 6, the reduction of absolute valueof GI resulted in the decrease of overshoot of M AP from18 . 6% to 13. 2% for the sensitive patients at the expenseof prolonging the rise-time of MAP from 100to 120 s fo rthe normal patients. This necessary compromise im-proved the stability of the fuzzy con trol SN P delivery sy s-tem for the sensitive patients while losing little dynamic

(24)-SNP(s) 1 + 40 s


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GE=O 25, GR=13 5. I = -0 06. T=10 s e cK = - 2 88, MAP s e t p o i n t = 100 m m Hg

a - - L=10b - - L = 1 6

14 0 140

GE=O 25 , GR=13 5, L=16. T=10 s e cK=-0 7 2 , MA P s e t p o i n t = 100 m m Hq

a - - GI=-0 08b - - GI=-0.06

100 / - 100I I I I80 I 80 I I I I I0 200 400 600 800 1000 0 200 400 600 800 1000 1200

t i m e ( s e c o n d ) t i m e ( s e c o n d )Fig. 4. The effect of increasing the value of L f rom 10 to 16 on the per-formance of the fuzzy controller regulating M A P in the sensitive patients( K = -2.88) based on compute r s imula t ion .

Fig. 6. The effect of decreasing the absolute value of GI f rom -0 .08 to-0.06 on the performance of the fuzzy co ntroller regulating M AP in thenormal patients ( K = -0 .72) based on compute r simula t ion .

GE=O 25. GR= 13 5, = 16, T= 10 s e cK=-2 88. MA P s e t p o i n t = 100 m m Hg

SNP infusion rate was less than zero. These measureswere similar to those used in [9].D . Clinical Setting

The fuzzy controller designed above was used to main-tain desired MAP in patients in the Cardiac Surgical In-tensive Care Unit (CICU) of the Carraway MethodistMedical Center. Fig. 7 is a block diagram of the imple-mented fuzzy control SNP delivery system. A Hewlett-Packard 78534 Monitor/Terminal was used to collect,v 120 process, and display MAP, systolic pressure, diastolica pressure, left atrial pressure, right atrial pressure, heart5 rate, and the electrocard iogram. A Puritan-Bennett 7200a

Microprocessor Ventilator was connected to the patientsto maintain respiration. MAP values were fed from theHewlett-Packard Monitor into an IBM PS/2 Model 70computer, ran the fuzzy controller in the form of the non-linear control algorithms encoded in C programming lan-2o o 4oo 6o o 800 , oo 2oo guage. S N P infusion rate calculated by the fuzzy control-ler was sent to an Abott/Shaw LifeCareTMPump Model4. T he pump infused SN P to patients.

160

a - - GI=-008b - - GI=-006

140,-.OII

Q

100

80

t i m e ( s e c o n d )F ig . 5 . Th e effect of decreasing the absolute value of GI from -0.08 to-0.06 on the performance of the fuzzy controller regulating M AP in thesensitive patients (K = -2 .88) based on compute r s imula t ion .

control performance for the normal patients. Further tun-ing in a clinical setting was necessary to achieve bettertransient and steady-state response.To improve patients ' safety, we limited the maximumincrement of SNP infusion rate to 7. 0 mL /h for any sam-pling time, overriding 9.6 mL/h imposed automatical lyby the fuzzy controller itself. We also set the incrementof SNP infusion rate to zero when MAP was more than20 mm Hg below the M AP setpoint and when calculated

Twelve postoperative patients who exhibited elevatedMAP following coronary artery bypass grafting proce-dures took part in the study. Typically the trials beganwithin 1-2 h after the patients arrived in CICU. The typ-ical MAP setpoint, determined by the attending medicaldoctors or the nurses, was 80 mm Hg . The fuzzy controlsystem was started by technical personnel when the at-tending nurses thought S NP was needed for a patient. Th efuzzy control system was always initiated at a SNP infu-sion rate of zero. T he technical personnel constantly mon-itored the operation of the control system. During the op-eration of the fuzzy control system, no special care wasgiven to the patient by the nurses.


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MEANARTERIAL

Patientuzzy control CRUjalgorithm PUMP

Fig. 7. Block diag ram of the fuzzy control SNP delivery system.

GE=0.25. GI=-0.06. L = 1 6 , T = 1 0 secK=-2.88. MA P setpoint = 100 m m Hg1 I I I I

a - - GR=8 0b- - GR=13 5

0 20 0 400 60 0 800 1000 1200time (second)

Fig. 8 . Comparison of M AP in the sensitive patients ( K = - 2 . 8 8 ) beforeand after increasing the value of GR from 8.0 to 13.5 based on compute rsimulation.

111. CL INICALE R F O R M A N C EF THE F U Z Z Y O N T R O LSNP DE L IVE RYYSTEMIn the first two patient trials, it was found that SNPinfusion rate was not regulated satisfactorily to handlerapid and large changes of M AP. We analyzed the resultsand concluded that the fuzzy controller did not increaseor decrease SN P infusion rate fast enough when MA P waschanging dramatically. The problem occurred due to in-adequate nonlinearity and lack of sensitivity of the fuzzycontroller with respect to the rate change of error of MA P.To achieve better results, the parameters of the fuzzycontroller chosen before the clinical trials should be mod-ified. The mathematical model of the patient described in

(24) was utilized to further tune the parameters of thefuzzy controller, especially GR, which scaled the ratechange of error of MA P. By varying the nonlinearity andsensitivity of the fuzzy controller with respect to ratechange of error of MAP for patients with different sensi-tivities, a larger GR value 13.5 was found w hich resultedin better control performance. Figs. 8an d 9 demonstratethe simulated results of the fuzzy control SNP deliverysystem for the sensitive patients ( K = - 2 . 8 8 ) and thenormal patients ( K = - 0 .72 ) , before and after GR was

GE=0.25, G1=-0.06. L=16, T = 1 0 secK=-0.72. MAP setpoint = 100 m m Hg

a - - GR=8.0b - - GR=13.5

80 I I I I I I I0 200 400 60 0 800 1000 1200time (second)

Fig . 9. Compar ison of M A P in the normal patients ( K = -0.72) beforeand after increasing the value of GR from 8.0 to 13 .5 based on computersimulation.

increased from 8.0 to 13.5. Obviously, the larger GRmade the fuzzy control system considerably more robust.Consequently, the performance of the fuzzy controller wassignificantly improved and better clinical results were ob-tained for the remaining ten patients.Fig. 10 shows a typical trend plot of both M AP and thecorresponding S NP infusion rate obtained from a fuzzycontroller controlled patient, after the larger GR was im-plemented. Fig . 11 illustrates how the nonlinear propor-tional gain Kpd nd integral gain Kidof the fuzzy controllercontinuously changed with time to cope with the nonlin-earities of the MAP response shown in Fig . 10, comparedto the constant proportional gain K p and integral gain K iof the PI controller.During the trials, all normal patient care duties wereperformed by the nurses. The duties included samplingpatient blood, suctioning the patient to clear hidher air-way, bathing the patient, changing bed linen, injectingdrugs other than SNP, infusing blood, and so on . MAPin the patient frequently fluctuated considerably when theabove-mentioned duties were being carried out. Sam plingblood normally caused MAP to jump up to a high value(say, 150 mm Hg) or down to a low value (say, 20 mm


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1067YING er a l . : FUZZY CONTROL OF MEAN ARTERIAL PRESSURE

patient number 6 MAP set oint = 80 mm Hg200 GE=0.25 GR= 3.5 G I = -O.& T= 0 sec, L=16 700

1% 150ns2 1wEE 100W

50 50

0 0T ime(a )

129.3 1398 1353 1498 1 5 1 3 1698 1653 1138 1823 1908 1 9 5 3T imeFig. 10. (a) MAP response for a single patient obtained by using the fuzzy control SNP delivery system clinically. (b) Thecorresponding SNP infusion rate. The patient had blood sampled at 12 :5 7 , 13 :4 2 , 1 5 :56 , and 17 :50 . Suctioning the patientbegan at 13 :04, 7 :00, nd 19: 17 . The patient was bathed between 1 5 : 36 to 15 :50 . Changing bed linen stated at 19:45 andlasted for several minutes. Injection of Valium took place at 13 :09, 14 :41 , and 17 :57. The drugs Pavulon and morphine wereinjected into the patient at 14 : 0 and 17 :10, respectively.

Hg) within a very short period of time. This temporaryfluctuation of MAP signal can be filtered by a digital fil-ter. Such a digital filter, however, was not used in ourtrials, but is planned for use in future studies. In thesetrials, the fuzzy controller was manually put into a holdmode right before blood was sampled. T he hold mode ofthe fuzzy controller ignored the MAP signal and sent theprevious SN P infusion rate as the current rate to the in-fusion pump. Fuzzy control resumed upon completion ofsampling. The fuzzy controller was always in operationwhen the patients were being injected with other drugs orinfused with blood. T he fuzzy controller was generally inoperation when the patients were being suctioned, bathed,or having bed linens changed. Suctioning, bathing, andchanging bed linen usually caused large fluctuation ofMAP, especially when such activities were prolonged.

The fuzzy controller was sometimes temporarily put intothe hold mode if the fluctuation of MAP was too large.The fuzzy control resumed immediately after the dutieswere performed. The patient whose M AP is shown in Fig.10had blood sampled blood at 12 :57,13 42,15 :56, nd17 50. Suctioning the patient began at 13:04, 17 00 nd19 :17. he patient was bathed between 15 :36 an d 15 50.Changing bed linen started at 19 :45 and lasted fo r severalminutes. Injection of Valium took place at 13 09, 14 4 1 ,an d 17:57.The drugs Pavulon and morphine were in-jected into the patient at 14 50 an d 17 10, respectively.Besides the situations listed above, other factors alsoaffected MAP. Substantial fluctuation of MAP took placeas body tem perature of the patients was changing or if thepatients were in pain. Spontaneous fluctuation of MAPoccurred as well. In addition to these, sensitivity of the


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1068 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. IO , OCTOBER 1992

patient number 6, MAP setpoint = 80 mm HgG E =0 .2 5, GR = 13 .5 , G I = - 0 . 0 6 , T = l O ~ ~ , L = 1 6

I 5 0

!:23 1308 1353 14:uI 1523 16.98 1653 17% 18:U 1908 1953TimeComparison of the nonlinear proportional gain Kpd f the fuzzycontroller to the constant proportional gain K!, of the corresponding PI con-troller ((Kpd- K,,) /K,) showed change of Kpdover time corresponding tothe nonlinearities in M A P for this patient. Change of K,d over t ime is thesame as that of Kpd since (Kid - K , ) / K , = (Kpd- K, , ) /K , .

TABLE I1MEAN p ) PERCENT OF TOTAL UZZY-CONTROLLER-RUNI M EAND STANDARD DEV IA TI ON) FORDIFFERENTAP INTERVALS.H ECALCULATIONS BASED N 12 PATIENT RIALS. AP, IS THE D E S I R E DMAP SETPOINT

1. 2 MAP,P 1 oo 3.92 89.31 3.85 I .92U 1.09 2.72 4.96 1.84 1.14

patients to SN P changed with time. T he response delay toSNP varied among the patients. N evertheless, as the re-sult shown in Fig. 10 illustrates, the fuzzy control SNPdelivery system regulated MAP satisfactorily even withthe fluctuation of M AP cau sed by the various facto rs statedabove. For this patient, the percentage of time in whichMA P stayed within the band between 90% and 1 10% ofthe MA P setpoint was 86.5 % . The trial lasted 7 h and 49min.The length of time that 12 patients were on the fuzzycontrol system ranged from 1 h 45 min to 18 h 7 min. Thetotal fuzzy-controller-run time was 95 h 13 min. T his in-cludes the time for the patient tr ials undertaken both be-fore and after the further tuning of the controller param-eters. The times fo r which SN P infusion rate was zero andthe patients own system was regulating MAP were ex-cluded. Time for which the fuzzy controller was put inthe hold m ode was also excluded. For the sam pling periodT = 10 s, 34 27 8 MAP samples were collected from thepatients. The overall performance of the fuzzy controlSN P delivery system in 12 patient trials is summarized inTable 11. The table exhibits that MA P is tightly controlledaround the desired MA P level.

IV . DISCUSSIONA wide variation of patient sensitivity to SN P was ex-perienced during the clinic al trials. E ven through differentpatient sensitivity resulted in different MAP response, itwas not estimated since the sensitivity was not needed bythe fuzzy controller. The fuzzy controller could cope withdifferent sensitivity by continuously adjusting its nonlin-ear proportional gain Kpdand integral gain Kid.To eval-uate the ability of the fuzzy control system handling thepatients with different sensitivity, computer simulationwas conducted by again using the patient model given in(24) . The simulated results illustrated in Fig. 12 indicatethat the clinically fine-tuned fuzzy control SNP systemcould adapt to a wide range of patient sensitivity, fromthe sensitive patients (K = -2 .88) to the insensitive pa-tients ( K = - 0 . 1 8 ) , a ratio of 16 : l . This range of sen-sitivity covers that of most patients [101.To enhance the performance of the fuzzy control SNPdelivery system, refinements are necessary. Some intel-ligent digital filters should be developed to identify andprocess different MAP waveforms generated by differentclinical activities such as suctioning the airway and


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YlNG er al. F UZZY CONTROL OF MEAN ARTERIAL PRESSUREGE-0 .25 . GR = 13 5. GI=-O 06. L= 16T = 1 0 s e c , MAP s e t p o i n t = 100 mm Hg

160 I I I I Ia - - K=-288b - - K = - Q 7 2C - - K = - 0 18

800 300 600 900 1200 1500 1800

t ime ( s e c o n d )Fig. 12. Simulated M AP for the sensitive patients (K = -2.88). the nor-mal patients ( K = -0.7 2) and the insensitive patients ( K = -0.18), usingthe clinically fine-tuned parameters of the fuzzy controller.

bathing the patient. It would be helpful to let the filtersguide the action o f the fuzzy controller and adjust the pa-rameters of the fuzzy controller on-line. Ad ditionally, thesafety measures and the warning system n eed to be mod-ified to further improve patient sa fety.V . CONCLUSION

Results of the clinical trials on 12 patients revealed thatthe performance of the fu zzy control S N P delivery systemwas clinically accep table. Based o n the clinical results andthe simulated results, we expect the fuzzy control SNPdelivery system to perform reasonably well for most pa-tients.The preliminary successful implementation of the non-linear control algorithms for controlling MAP in patientsshows effectiveness in a case involving nonlinearity, time-delay, and time-variance. Therefore, the algorithmsshould be effective on other physiological variables in-volving these factors.ACKNOWLEDGMENT

Thanks to Dr. D. M. Tucker, Dr. A. W . Stanley Jr.,Dr. C. L. Athanasuleas and M. Per1 at Carraway Meth-odist Medical Center for their help. Thanks also to K .Elder for her proofreading and helpful comments on themanuscript.REFERENCES[ I ] D. M. Cosgrove 111, J . H. Pe t re, J. L. Walle r , J . V. Roth , C . Shep-herd, and L. H . Cohn, Automated control of postoperative hyper-tension: A prospective, randomized multicenter study, Ann. Thorac.Surg . , vol . 47 , pp . 678-683, 1989.

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[2] R. A . de Asla, A. M. Benis, R. A . Jurado, and R. S . Litwak, Man-agement of postcardiotomy hypertension by microcomputer-con-trolled administration of sodium nitropru sside, J . Thorac. Curdio-vasc . Surg . , vol. 89, pp. 115-120, 1985.[3 ] 1. J . Hammond, W. M. Kirkenda ll , and R . V. Calfee, Hypertensivecrisis managed by compu ter controlled infusion of sodium nitroprus-side: A model for the closed loop administration of short actingvasoactive agents, Comput. Biomed . Res . , vol. 12, pp. 97-108,1979.141 E. H. Mamdan i, App lication of fuzzy algorithms for control of sim-ple dynamics plant, Proc. IEE, vol. 121, no. 12, 1974.[5 ] J . F. Mar t in , A. M . Schne ide r , and N . T. Smith, Multiple-modeladaptive control of blood pressure using so dium nitroprusside, IEEETrans. Biomed. Eng . , vol . 34 , pp . 603-611, 1987.161 L. I. Meline , D. R . Westenskow, N . L. Pace, and M. N . Bodi ly ,Computer-controlled regulation of sodium nitroprusside infusion,Anes th . An a lg . , vol. 64, pp, 38-42, 1985.171 J . S . Packer , D. G. Mason, and J . F. Cade, and S . M. McKinley ,An adaptive controller for closed-loop management of blood pres-sure in seriously ill patients, IEEE Trans. Biomed. Eng. , vol . 34 ,[8] J. H. Petre, D. M. Cosgrove, and F. G. Estafanous, Closed loopcomputerized control of sodium nitroprusside, Trans. Amer. Soc.Artif. Intern. Organs, vol . XXXIX, pp . 501-505, 1983.[9 ] L. C . Shepphard, Computer control of the infusion of vasoactivedrugs, Ann. Biomed. En g . , vol. 8, pp. 431-444, 1980.

[lo] J . B. Slate, M odel-based design of a controller for infusion sodiumnitroprusside during postsurgical hypertension, Ph .D . thesis, Univ.Wisconsin-Madison, 1980.[ I l l J. B. Slate, L. C . Sheppard, V . C. R ideout , and E. H. Blackstone,A model for design of a blood pressure controller for hypertensive

patients, 5th IFAC Symp. Identif ication Syst. Parameter Estima-tion, Darmstadt, F. R . Germany, Sept. 24-28, 1979.1121 J . Slate and L. C . Sheppard, A utomatic control of blood pressureby drug infusion, IEE Proc . , vol . 129, p t . A, no . 9 , 1982.[I31 G . I. Voss, P. G. Katona, and H. J. Chizeck, Adaptive multivari-able drug delivery: control of arterial pressure and cardiac output inanesthetized dogs, IEEE Trans. Biomed. Eng. , vol. 34, pp. 617-623, 1987.[ 141 M . Sugeno, Ed. Industrial applications offu zzy c ontrol. North-Hol-land: Elsevier , 1985.[I51 H. Ying, W . M. S i le r , and D. M. Tucker , A new type of fuzzycontroller based on fuzzy expert system shell SLO PS, Proc. IEEEInternut. Workshop on Expert Syst. App. Industry, Japan, May 1988.[161 H . Ying, L. C. Sheppard . and D. M. Tucker , Exper t - system-basedfuzzy control of arterial pressure by drug infusion, MedProg. Tech-

nol., vol. 13, pp. 202-215, 1988.1171 H. Ying and L. C. Sheppard, Real- time ex pert-system-based fuzzycontrol of mean arterial pressure in pigs with sodium nitroprussideinfusion, Med. Prog . Techno l . , vol. 16, pp. 69-76, 1989.[18] H. Ying, W . M. Siler , and J. J. Buckley, Fuzzy control theory: Anonlinear case, Automarica, vol. 26, pp. 513-520, 1990.1191 L . A . Zadeh, Fuzzy sets, Information Conrr., 1965.

pp. 612-616, 1987.

Ha o Ying (S88-M91) was born in Shanghai,China, on Dec. 11, 1958. He received B.S. andM.S. degrees in electr ical engineering from ChinaTextile University, Shanghai, in 1982 and 1 984,and the Ph.D. degree in biomedical engineeringin 1990 from the University of Alabama at Bir-mingham. While studying for the Ph.D. degree,he worked as a R esearch Fellow in the Kemp-Car-raway Heart Institute and as an Instructor in theDepartment of Mathematics at UAB.He is presently an assistant professor in the De-partment of Physiology and Biophysics, University of Texas MedicalBranch. His research interests include theory and app lication of fuzzy co n-trol, and application of expert systems and neural networks. Th e focus ofhis current research is on intelligent control in biomedical environ ments.


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1070 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39. NO . 10, OCTOBER 1992

Michae l McEachern received the B. A. degree in1966 and the M.A . degree in 1968 from Califor-nia State Universi ty, Sacra mento with a special i tyin archeology.He has worked on various archeological proj-ects in the US, Canada, and Mexico. He beganworking with the Departm ent of Anthropology atthe Universi ty of Alabama, Birmingham , in 1977using computers to analyze archeological mate-rials. H e has been with Carraway Me thodist Med-ical Center s ince 1981 developing software usedin the cl inical environment .Donald W . Eddleman (M87) was born in KeyWest , FL, on June 8, 1963. He received the B.S.degree in computer science from Southern Col-lege of Technology, GA in 1987.Since 1987 he has been with Carraway Meth-odist Medical Center implementing a real-t imeobject-oriented device-monitoring system for usein a cardiac surgery intensive care uni t .Mr. Eddleman is a member of the IEEE PI073standards committee which is developing a familyof s tandards to provide open systems communi-cat ion in heal th care applicat ions.

Louis C . Sheppard (SM79-F92) was born inPine Bluff, AR, on May 28, 1933 He receivedthe B S . degree in chemical engineering from theUniversity of Arkansas in 1957 and the Ph. D de-gree in elec tncal engineering from the Universityof London, Imperial College of Science, Tech-nology and Medicine, in 1976.He is now Associate Vice President for Re-search and Director of the Biomedical Engineer-ing Center at the University of Texas MedicalBranch at Galveston (UTM B) He has facul ty ap-pointments as Professor of Physiology an d Biophysics at UTM B, Professorof Biomedical Engineering at the University of Texas at Austin and Ad-junct Professor of Electn cal Engineering at the University of Houston From1966 until 1988 while a mem ber of the faculty of the Department of S ur-gery at the Universi ty of Alabama at Birmingham (UAB) he wa s develop-ing and implementing computer-based systems for intensive care that in-cluded automated blood and drug infusion for closed-loop, feedback controlof cardiac and vascular pressures From 1979 through 1988 he was the firstChairman of the Department of Biomedical Engineering at UAB. His ex-penenc e in industry exceeded nine years , s ix years (1957-1963) in petro-chemicals (Diamond Sham rock) and over three years (1963-1966) in med-ical com puting (International Business Mach ines)Dr Sheppard is a Registered Professional Engineer In Texas and Ala-bama

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Fuzzy Controler MAP